function [mean_sumX,std_sumX] = CalcTimeSeriesSumVol(X,prob_X,Phi_X,n,Phi_X_n)
% computes std(X(t+m)+X(t))
    
    if nargin<=4
        Phi_X_n = mpower2(Phi_X,n);
    end
    
    mean_X = sum(prob_X(:).*X(:));
    var_X = sum(prob_X(:).*(X(:).^2)) - mean_X^2;

    mean_sumX = 2*mean_X;
    
    condE_X_n = Phi_X_n*X(:);
    var_sumX = 2*var_X + 2*(sum(prob_X(:).*X(:).*condE_X_n) - mean_X^2);
    std_sumX = sqrt(var_sumX);


end